# conding=utf-8

"""
Given a binary tree, determine if it is a valid binary search tree (BST).

Assume a BST is defined as follows:

    The left subtree of a node contains only nodes with keys less than the node's key.
    The right subtree of a node contains only nodes with keys greater than the node's key.
    Both the left and right subtrees must also be binary search trees.

Example 1:

Input:
    2
   / \
  1   3
Output: true

Example 2:

    5
   / \
  1   4
     / \
    3   6
Output: false
Explanation: The input is: [5,1,4,null,null,3,6]. The root node's value
             is 5 but its right child's value is 4.


"""

# Definition for a binary tree node.
# class TreeNode(object):
#     def __init__(self, x):
#         self.val = x
#         self.left = None
#         self.right = None

class Solution(object):
    def isValidBST(self, root):
        """
        :type root: TreeNode
        :rtype: bool
        """
        return self.isValidBSTRecur(root, float("-inf"), float("inf"))

    def isValidBSTRecur(self, root, low, high):
        if root is None:
            return True

        return low < root.val < high and self.isValidBSTRecur(root.left, low, root.val) and self.isValidBSTRecur(root.right, root.val, high)
